Why does Paul address the church as “the church of God” rather than “the church of Christ”? (1 Cor. 1:2; 2 Cor. 1:1) In these passages he is speaking to all the saints. Aren’t the saints the church of Christ?
Christ IS God (John 1:1, 14). Therefore, the terms “church of Christ” and “church of God” mean the same thing from a biblical standpoint. The church which belongs to Christ belongs to God. That church would be the one who penitently and faithfully strives to follow only rightly divided Scripture in all its teachings and practices, which is why it is the church one reads about in the New Testament.
The term “church of Christ” is not the only biblical name or description given to the New Testament church (cf. 1 Cor. 1:2; Acts 9:2; Heb. 12:23; 1 Thess. 1:1; etc.) In like manner, a church could have a biblical name or description and still unrepentantly practice and teach that which is not found in the Bible.
The term “saints” comes from the Greek word hagios, which literally means “most holy thing” or “one sanctified.” One is sanctified through baptism into the church of Christ (1 Cor. 6:11; 12:13; cf. Eph. 1:22-23). Therefore saints make up the church/assembly/ekklesia of Christ, the church of God, the Lord’s church.